[unreadable] Our broad long-term goal is to develop and optimize statistical reconstruction for emission computed tomography (ECT). One goal is the development of fast iterative MAP (maximum a posteriori) reconstruction algorithms. A second goal is the development of theoretical methods to rapidly optimize the MAP reconstruction to maximize performance on a variety of lesion detection tasks for SPECT. The two goals are linked in that scalar figures of merit for lesion detection in MAP-reconstructed images can be quickly calculated by our theoretical means. While our aims focus on SPECT, our fast reconstruction algorithms can also be used for PET. We shall continue our development of fast convergent, ordered-subset MAP algorithms that free the user from setting hand-tuned parameters such as the relaxation schedules needed by competing approaches. We will also develop, for SPECT, theoretical expressions that incorporate MAP objectives and model observers to predict lesion detection performance by human observers. Established model-observer-based methods that use many sample reconstructions can also do this, but our theoretical methods can be 2 to 4 orders of magnitude faster. This speed allows a user to quickly optimize lesion detection with respect to these reconstruction parameters: degree of regularization, choice of prior model, and system model error in geometric response, attenuation and scatter correction. Attenuation and scatter correction modeling require that we develop methods to propagate the noisy estimates of scatter or attenuation into the system model. This fast evaluation of image quality allows one to narrow the parameter ranges that control image quality, so that human ROC studies can be applied with this reduced parameter set. For SPECT, we have developed analytic means for predicting detection figures of merit for MAP reconstructions of signal-known-exactly/background-known-exactly objects, but we propose to extend our methods to a variety of more realistic cases including signal-location unknown and variable signal size. Background variability affects detection, and we propose to use real statistical background models derived from autoradiographic animal data to explore this issue. We shall validate methods using sample and human observer studies. Our contributions lie in new methodologies for optimization of reconstructions for lesion detection and in easy-to-use fast reconstruction methods. [unreadable] [unreadable]